OFFSET
0,1
COMMENTS
Ramanujan's question 754 in the Journal of the Indian Mathematical Society (VIII, 80) asked "Show that exp(x) * x^(-x) * Pi^(-1/2) * Gamma(1 + x) = (8*x^3 + 4*x^2 + x + E)^(1/6), where E lies between 1/100 and 1/30 for all positive values of x".
A numerical search provides an approximate minimum of E = 0.010045071877... (A319459) at x = 0.6715..., confirming Ramanujan's lower bound.
LINKS
B. C. Berndt, Y. S. Choi, S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., 236 (1999), 15-56, DOI: 10.1090/conm/236 (see Q754, JIMS VIII).
B. C. Berndt, Y. S. Choi, S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q754, JIMS VIII).
EXAMPLE
0.6715037657680253608648120575402300347350320701806081836583...
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Sep 19 2018
STATUS
approved